Summary

Hartree-Fock-Bogolyubov solutions corresponding to the tetrahedral deformation were found in six tetrahedrally doubly-magic nuclei: $^{80}$Zr, $^{98}$Zr, $^{110}$Zr, $^{126}$Ba, $^{160}$Yb, and $^{226}$Th. Results with four Skyrme forces, SLy4, SkM*, SIII, and SkP, sometimes significantly differ in the values of $\beta _{32}$, depths of the tetrahedral minima, and their energies with respect to the co-existing quadrupole solutions. The inclusion of pairing reduces the depths, or even suppresses the existence of the tetrahedral minima. In Zr isotopes, the tetrahedral minima are rather shallow, but some forces predict them as the lowest in energy. In $^{126}$Ba, they are not lower than 7MeV above the quadrupole solutions, but in $^{160}$Yb and $^{226}$Th that minimum distance is reduced to 3MeV. Tetrahedral minima in $^{126}$Ba, $^{160}$Yb, and $^{226}$Th are estimated to be deeper than in the Zr isotopes.